Tool · Playground
Map composer
Build new 1D maps by composing two known ones. Pick F and G, pick the order or blend, then explore the resulting dynamics: cobweb, time series, bifurcation, Lyapunov exponent.
F
f(x) = r·x·(1 − x)G
f(x) = μ · min(x, 1 − x)Composition
Orange curve: composed map y = h(x). The cobweb walks x → h(x) → diagonal → x, …
Things to try
- Logistic ∘ tent: composing a smooth quadratic with a piecewise-linear map gives a non-trivial unimodal landscape with a shifted bifurcation cascade.
- Chebyshev ∘ Chebyshev: Chebyshev maps are topologically conjugate to logistic at r=4. Composing them stays chaotic but reshapes the invariant measure.
- Linear blend α·F + (1−α)·G: sweep α and watch the bifurcation skeleton morph between two distinct routes to chaos.
- G ∘ F vs F ∘ G: they share Lyapunov sign asymptotically but produce different invariant densities. Toggle and compare.
Compare with the simpler logistic playground and the bifurcation tool.
FAQ